A Tight Bound for Hypergraph Regularity

Computer Science/Discrete Mathematics Seminar I
Topic:A Tight Bound for Hypergraph Regularity
Speaker:Guy Moshkovitz
Affiliation:Harvard University
Date:Monday, February 26
Time/Room:11:00am - 12:15pm/Simonyi Hall 101
Video Link:https://video.ias.edu/csdm/2018/0226-GuyMoshkovitz

The hypergraph regularity lemma — the extension of Szemeredi's graph regularity lemma to the setting of k-graphs — is one of the most celebrated combinatorial results obtained in the past decade. By now there are various (very different) proofs of this lemma, obtained by Gowers, Rodl et al. and Tao. Unfortunately, what all these proofs have in common is that they yield partitions whose order is given by the k-th Ackermann function.
 
We prove that such Ackermann-type bounds are unavoidable for every k>=2, thus confirming a prediction of Tao. Prior to our work, the only result of this kind was Gowers' famous lower bound for graph regularity.